I had the honor to give one of four tutorials at the 2016 Center for Turbulence Research Summer Program. The aim of the tutorial was to discuss the thermodynamics of supercritical fluids and its implications for high-pressure liquid-fueled combustion systems, to expose the state-of-the-art of physics modeling, and finally, to motivate the need to develop thermodynamically consistent models based on the equations of fluid motion to further investigate transcritical phenomena. [video] [slides]